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\title{Solutions to 2010 (May be incorrect)}

\begin{document}
\maketitle

1.

(a)

(b)

(c)

(d)

We will use $F$ to denote frowning, $E$ for eyebrow, $J$ for joy and
$S$ for sadness. We wish to find $P(J|F)$.

We know the following probabilities,

$$
P(F|S) = 0.9 \quad
P(E|J) = 0.8 \quad
P(J) = 0.7 \quad
P(S) = 0.3
$$

Consider Bayes Theorem which states that for probabilities $A$ and $B$

$$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$

This can be written in the form
$$P(B|A) = \frac{P(A \cap B)}{P(A)}$$

Therefore to find  $P(J|F)$ we need to know the probabilities $P(F)$
and $P(J \cap F)$. We can work this out using the following table
which is based on the provided probabilities and the rearrangement of
the above formula such that 
$$P(A \cap B) = P(B|A)P(A)$$

\begin{tabular}{c | c c c}
        | & $J$  & $S$ & $J \cup S$ \\
\hline   
$E$       &0.56  &0.03 & 0.59   \\ 
$F$       &0.14  &0.27 & 0.41   \\
$E \cup F$&0.7   &0.3   & 1
\end{tabular}

We now know $P(F) = 0.41$ and $P(J \cap F) = 0.14$
$$P(J|F) = \frac{P(J \cap F)}{P(F)} = \frac{0.14}{0.41} \sim=0.34$$

2.

(a)
Percepts
\begin{itemize}
\item Visual feed from camera
\item Audio feed from microphone
\item Speech 
\item Faces
\item Body poses
\end{itemize}

Actions
\begin{itemize}
\item Animate characters
\item Change music
\item Video control
\end{itemize}

(b)
A \emph{utility function} is a mapping from a state to a real number
describing the associated degree of ``happiness'' of this
state. ``Happiness'' is a measure of how desirable this state is
according to the agents performance metric.

For this agent's utility function should be tied into how confident
the agent is in recognizing an interaction. For instance if similar
gestures are used to change track and increase volume, the action used
should be tied to the confidence that the agent has in classifying any
particular percept.

Experts could be used to refine this utility function by ensuring that
percepts are easily classified such that they can be easily
distinguished from each other and from normal human behavior (not
meant to interact with the agent).

(c)
\begin{description}
\item{Recognize spoken commands}
  Speech recognition would be required to understand what is being
  said by the user. Natural language processing would then be required
  to understand what the user is trying to say. This is useful to the
  user as they do not need to press buttons or move to interact with
  the agent and can provide a more natural control experience. 
\item {Suggest similar music/television/movies}
  After a user has listened to music, the agent could suggest similar
  music based on machine learning techniques. This could be useful if
  the agent is trying to sat a particular mood.
\item {Fitness instructor}
  The agent could suggest a workout for a user and monitor their
  progress by recognizing body poses. It may be able to identify
  incorrect poses and demonstrate using animated characters how to do
  the pose properly. This is useful for fat users.
\end{description}

(d)

Noise reduction, ambiguity 

(e)

VPI - work out what is the most important information and focus
questions based on that.

3. 

(a)

Russel and Norvig define a rational agent to be an agent which 

``For each possible percept sequence, a rational agent should select
an action that is expected to maximizer it's performance measure,
given the evidence provided by the percept sequence and whatever built
in knowledge the agent has''

(Artificial Intelligence: A modern approach)

The rational approach attempts to choose actions based on some ideal
version of intelligence, rather than attempting to mimic human
intelligence.

It is often hard to be perfectly rational as that requires a perfect
performance measure for any action and may be too time-consuming to
work out the optimal action, therefore a less rational action may be
chosen to satisfy this constraint.

(b)
Fucked if I know

(c)

Uninformed search uses no additional domain knowledge other than that
which is encoded in the problem itself. Informed search can use
additional world knowledge to form a heuristic function. 

Uninformed
Breadth-first, Depth first

Informed
$A^*$ search, greedy

(d)

Machine learning is the idea that the agent will critic received
feedback to tune it's performance measure so that any future actions
can influence the utility of future choices. It is needed otherwise
the agent is completely dependent on built in agent and is unable to
(realistically) act autonomously and adapt to know situations. Google
searches and Amazon recommends.

(e)

The ``Turing test'' is a test proposed by Alan Turing in his 1950's
paper ``Computing Machinery and Intelligence''. It is a test to
determine whether a being that is known to be intelligent (a human)
can distinguish between two opponents to determine which is human and
which is an artificial intelligence.


(f)

Draw a sketch of a ``sigmoind-like neuron unit''yourself. Twat.



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